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Simplifying 3a2 + -7a + 6 + -4a2 + -3a + 4 = 0 Reorder the terms: 6 + 4 + -7a + -3a + 3a2 + -4a2 = 0 Combine like terms: 6 + 4 = 10 10 + -7a + -3a + 3a2 + -4a2 = 0 Combine like terms: -7a + -3a = -10a 10 + -10a + 3a2 + -4a2 = 0 Combine like terms: 3a2 + -4a2 = -1a2 10 + -10a + -1a2 = 0 Solving 10 + -10a + -1a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -10 + 10a + a2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + 10a + 10 + a2 = 0 + 10 Reorder the terms: -10 + 10 + 10a + a2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 10a + a2 = 0 + 10 10a + a2 = 0 + 10 Combine like terms: 0 + 10 = 10 10a + a2 = 10 The a term is 10a. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10a + 25 + a2 = 10 + 25 Reorder the terms: 25 + 10a + a2 = 10 + 25 Combine like terms: 10 + 25 = 35 25 + 10a + a2 = 35 Factor a perfect square on the left side: (a + 5)(a + 5) = 35 Calculate the square root of the right side: 5.916079783 Break this problem into two subproblems by setting (a + 5) equal to 5.916079783 and -5.916079783.Subproblem 1
a + 5 = 5.916079783 Simplifying a + 5 = 5.916079783 Reorder the terms: 5 + a = 5.916079783 Solving 5 + a = 5.916079783 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + a = 5.916079783 + -5 Combine like terms: 5 + -5 = 0 0 + a = 5.916079783 + -5 a = 5.916079783 + -5 Combine like terms: 5.916079783 + -5 = 0.916079783 a = 0.916079783 Simplifying a = 0.916079783Subproblem 2
a + 5 = -5.916079783 Simplifying a + 5 = -5.916079783 Reorder the terms: 5 + a = -5.916079783 Solving 5 + a = -5.916079783 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + a = -5.916079783 + -5 Combine like terms: 5 + -5 = 0 0 + a = -5.916079783 + -5 a = -5.916079783 + -5 Combine like terms: -5.916079783 + -5 = -10.916079783 a = -10.916079783 Simplifying a = -10.916079783Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.916079783, -10.916079783}
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